HOW ACCURATE IS THE STREAMLINE DIFFUSION FINITE-ELEMENT METHOD

We investigate the optimal accuracy of the streamline diffusion finite element method applied to convection-dominated problems. For linear/b ilinear elements the theoretical order of convergence given in the lit erature is either O(h(3/2)) for quasi-uniform meshes or O(h(2)) for so me uniform meshes. The determination of the optimal order in general w as an open problem. By studying a special type of meshes, it is shown that the streamline diffusion method may actually converge with any or der within this range depending on the characterization of the meshes.